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bayesm.HART

bayesm.HART implements MCMC routines for hierarchical models with Hierarchical Additive Regression Trees (HART) priors, as developed in Wiemann (2025).

In the hierarchical logit specification, HART models the representative consumer as a flexible function of observed characteristics. This generalizes conventional hierarchical specifications that use a linear projection on a small set of characteristics. The same framework supports prediction for new consumers and posterior updating for consumers with accumulating choice histories.

See the corresponding working paper Personalization with HART for further discussion and details.

bayesm.HART builds on bayesm and BART. The syntax for estimating the HART logit model mirrors bayesm syntax. In many existing bayesm workflows, the main change is the Prior specification.

Installation

Install the latest development version from GitHub (requires devtools package):

if (!require("devtools")) {
  install.packages("devtools")
}
devtools::install_github("thomaswiemann/bayesm.HART", dependencies = TRUE)

Example

The following example applies the HART logit model to the Allenby and Ginter (1995) bank conjoint dataset. The first code block loads the data, formats the list structure required by rhierMnlRwMixture, and sets MCMC hyperparameters. This setup syntax is the same in bayesm and bayesm.HART.

# Load bayesm.HART for the sampler; load bayesm for the bank data
library(bayesm.HART)
library(bayesm)

# Load and prepare data from the 'bank' dataset (same as bayesm)
data(bank)
choiceAtt <- bank$choiceAtt
hh <- levels(factor(choiceAtt$id))
nhh <- length(hh)
lgtdata <- vector("list", length = nhh)
for (i in 1:nhh) {
    y = 2 - choiceAtt[choiceAtt[,1]==hh[i], 2]
    nobs = length(y)
    X_temp = as.matrix(choiceAtt[choiceAtt[,1]==hh[i], c(3:16)])
    X = matrix(0, nrow = nrow(X_temp) * 2, ncol = ncol(X_temp))
    X[seq(1, nrow(X), by = 2), ] = X_temp
    lgtdata[[i]] = list(y=y, X=X)
}
Z <- as.matrix(bank$demo[, -1]) # omit id
Z <- t(t(Z) - colMeans(Z)) # de-mean covariates as required by bayesm

# Final data object (same as bayesm)
Data <- list(lgtdata = lgtdata, Z = Z, p = 2)

# MCMC hyperparameters (same as bayesm)
Mcmc <- list(R = 2000, keep = 2, nprint = 500)

To fit the HART logit model, call rhierMnlRwMixture. Relative to a linear hierarchical specification, the main change is adding the bart entry in Prior. For illustration, the code below uses 50 trees per factor and leaves other hyperparameters at defaults. See ?rhierMnlRwMixture for details.

# Fit the HART logit model
if (!model_cache_ok) {
  out <- bayesm.HART::rhierMnlRwMixture(
      Data = Data, Mcmc = Mcmc, 
      Prior = list(
        ncomp = 1, 
        bart = list(num_trees = 50) # new HART prior parameters
        ),
      r_verbose = F # suppress R print output (optional)
  )
  saveRDS(list(out = out, generated_at = Sys.time()), model_cache_file)
}

With posterior draws from the fitted model, we can summarize any estimand. A central object is the representative respondent, i.e., expected part-worths conditional on respondent characteristics. The following code computes posterior means and standard deviations for three credit card attributes.

DeltaZ_hat <- predict(out, newdata = list(Z = Z), type = "DeltaZ+mu", 
                      burn = 250, r_verbose = FALSE)

posterior_mean <- apply(DeltaZ_hat, 2, mean)
posterior_sd <- apply(DeltaZ_hat, 2, sd)

# Indices for the desired coefficients:
# 2: Interest Low Fixed
# 8: Annual Fee Low
# 10: Bank Out-of-State
selected_indices <- c(2, 8, 10)

# Create a matrix with means and sds as rows
results_matrix <- rbind(
  `Posterior Mean` = posterior_mean[selected_indices],
  `Posterior SD`   = posterior_sd[selected_indices]
)

# Convert to a data frame and set column names
results_df <- as.data.frame(results_matrix)
colnames(results_df) <- c("Interest Low Fixed", "Annual Fee Low", "Bank Out-of-State")

# Print the data frame to the console
print(results_df, digits = 3)
#>                Interest Low Fixed Annual Fee Low Bank Out-of-State
#> Posterior Mean              5.047          4.152            -3.378
#> Posterior SD                0.902          0.901             0.989

Learn More about bayesm.HART

See the bayesm.HART vignettes:

Acknowledgements

bayesm.HART originated as a fork of the bayesm and BART packages. Its current implementation heavily leverages the codebase and foundational work from both packages. I gratefully acknowledge the contributions of their respective authors:

  • bayesm: Peter Rossi
  • BART: Robert McCulloch, Rodney Sparapani, Robert Gramacy, Matthew Pratola, Charles Spanbauer, Martyn Plummer, Nicky Best, Kate Cowles, Karen Vines

References

Allenby, Greg M. and James L. Ginter (1995). “Using Extremes to Design Products and Segment Markets.” Journal of Marketing Research 32.4, pp. 392–403.

Chipman, Hugh A., Edward I. George, and Robert E. McCulloch (2010). “BART: Bayesian Additive Regression Trees.” Annals of Applied Statistics 4.1.

Rossi, Peter E., Greg M. Allenby, and Robert McCulloch (2009). Bayesian Statistics and Marketing. Reprint. Wiley Series in Probability and Statistics. Chichester: Wiley.

Rossi, Peter (2023). bayesm: Bayesian Inference for Marketing/Micro-Econometrics. Comprehensive R Archive Network.

Sparapani, Rodney, Charles Spanbauer, and Robert McCulloch (2021). “Nonparametric Machine Learning and Efficient Computation with Bayesian Additive Regression Trees: The BART R Package.” Journal of Statistical Software 97, pp. 1–66.

Wiemann, Thomas (2025). “Personalization with HART.” Working paper.